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Features of the Nyström method for the Sherman-Lauricella equation on Piecewise Smooth Contours

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Author

Summary, in English

The stability of the Nyström method for the Sherman-Lauricella equation on contours with corner points $c_j$, $j=0,1,...,m$ relies on the invertibility of certain operators $A_{c_j}$ belonging to an algebra of Toeplitz operators. The operators $A_{c_j}$ do not depend on the shape of the contour, but on the opening angle $\theta_j$ of the corresponding corner $c_j$ and on parameters of the approximation method mentioned. They have a complicated structure and there is no analytic tool to verify their invertibility. To study this problem, the original Nyström method is applied to the Sherman-Lauricella equation on a special model contour that has only one corner point with varying opening angle $\theta_j$. In the interval $(0.1\pi,1.9\pi)$, it is found that there are $8$ values of $\theta_j$ where the invertibility of the operator $A_{c_j}$ may fail, so the corresponding original Nyström method on any contour with corner points of such magnitude cannot be stable and requires modification.

Department/s

Publishing year

2011

Language

English

Pages

403-414

Publication/Series

East Asian Journal on Applied Mathematics

Volume

1

Issue

4

Document type

Journal article

Publisher

Global Science Press

Topic

  • Mathematics

Keywords

  • Sherman-Lauricella equation
  • Nyström method
  • stability

Status

Published

Research group

  • Harmonic Analysis and Applications
  • Harmonic Analysis and Applications

ISBN/ISSN/Other

  • ISSN: 2079-7370